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In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density
estimation techniques in the context of compositional data analysis. Indeed, they gave
two options for the choice of the kernel to be used in the kernel estimator. One of
these kernels is based on the use the alr transformation on the simplex SD jointly with
the normal distribution on RD-1. However, these authors themselves recognized that
this method has some deficiencies. A method for overcoming these dificulties based on
recent developments for compositional data analysis and multivariate kernel estimation
theory, combining the ilr transformation with the use of the normal density with a full
bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-
Figueras (2006). Here we present an extensive simulation study that compares both
methods in practice, thus exploring the finite-sample behaviour of both estimators
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